What is ∞ + ∞ = ????

[Jarrey]

I have wondered if { [1,2,3,4..., ∞] = ∞ } + { [1,2,3,4..., ∞] = ∞ } is  two ∞ cardinaility series joined together. I mean, simply, cardinality of { [1,1,2,2,3,3,4,4...; ∞,∞] } which is twice the infinite series, if that makes any sense.

Don't mind me.


EDIT: apparently it's simply called a multiset.

In set theory, any element can only occur once, so,

{a,b,c} + {a,b,c,d} will result in (a,b,c,d}

If you want multiple occurrences it is called an mset or bag; which may apply to your example.